A new molecular motor is theoretically constructed from a double-walled carbon nanotube whose inner tube is a long (8,4) single-walled carbon nanotube (SWNT) and whose outer tube a short (14, 8) SWNT. The interaction between the inner and outer tubes is derived by summing the Lennard-Jones potentials between atoms in the inner and outer tubes. It is proved that the molecular motor in a thermal bath exhibits a directional motion with the temperature variation of the bath.